Algorithmic description of hippocampal granule cell dendritic morphology
Introduction
An intriguing question in hippocampal cellular neuroanatomy research is whether or not the dendritic morphology of principal cells can be captured by a concise, local-rule-based statistical model that allows for its implementation as a simple computational algorithm [1], [2]. The present work gives a positive answer to this problem. More precisely, here the dendritic morphology of the rat dentate gyrus granule cells is described accurately in all its functionally relevant statistical details by an elegant hidden-Markov (i.e., feed-forward, local and causal) algorithm. In addition, the hidden variables of the algorithm allow for plausible biophysical interpretations.
Section snippets
Materials and methods
Digital data of reconstructed rat dentate gyrus granule cells [4], [5] were kindly made available by Claiborne (University of Texas at San Antonio) through the Internet (www.utsa.edu/claibornelab). In these data files, neurons are represented as binary tree structures constructed with a finite set of cylindrical segments, each with an individual parent in the path to the root (soma), and with 0, 1, or 2 “daughter” segments at the opposite end (constituting termination, continuation, or
Simulation results
Two examples of virtual granule cells are represented in Fig. 2C and D, as compared to the real granule cells (Fig. 2A and B). Note the unequal path length distribution in dendrograms of real cell A, B, which reflects biological variations along the transversal axis of the dentate gyrus [4], [5]. This detail is well captured by the pair of virtual morphologies (Fig. 2C and D).
The good visual agreement of all essential morphological features between the two pairs of cells is further confirmed by
Discussion and conclusions
In this work we showed that the task of describing the shape of dentate gyrus granule cells computationally can be solved with an elegant hidden-Markov algorithm. The hidden variables of the algorithm include the expected number of terminal tips of a subtree and the path distance from the soma. These variable have a simple, if speculative, biophysical interpretation. We suggest that the variable m, determining the number of terminations in a subtree, can be related to the number of microtubules
Acknowledgements
The authors are indebted to Dr. Brenda Claiborne for sharing the neuronal reconstruction digital files and to Dr. Stephen Senft for valuable discussions and feedback on previous versions of the manuscript. This work was supported in part by Human Brain Project Grant R01 NS39600, funded jointly by NINDS, NIMH (National Institutes of Health), and the National Science Foundation.
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